Nonclassical effects in the second harmonic generation

The higher-order nonclassical squeezing and quantum entanglement effects emerging from the second harmonic generation of the associated two-mode and two-photon Hamiltonian are investigated in the dispersive limit. The squeezed states of the field, including the normal and amplitude squared (higher-order) squeezing factors are generated in two ways, i.e., from the bosonic operators via amplitude powered quadrature variables, and through the SU(2) characterization of a passive and lossless device with two input and two output ports, which then allows one to visualize the operations of beam splitters and phase shifters as rotations of angular momentum operators in 3-space. Two criteria for intermodal higher-order quantum entanglement and different coherent states for the two modes in the initial state are used to compute these nonclassical effects. The unitary time evolution of the linear entropy, computed from the partial trace of the density matrix over the secondary mode, is also used as a criterion of quantum entanglement. These approaches show, in fact, that the present model exhibits a considerable amount of this nonclassical effect. The unitary time evolution of the linear entropy shows that the present nonlinear optical model does not preserve the modulus of the Bloch vector.